Prove: if f is continuous, monotonic, and integer-valued only at integer arguments, then ⌊f(⌊x⌋)⌋ = ⌊f(x)⌋.

Analyze the prove: if f is continuous, monotonic, and integer-valued only at integer arguments, then ⌊f(⌊x⌋)⌋ = ⌊f(x)⌋..

Examples
Input: "test_input_1"
Output: "output_1"
Hints

Prove: if f is continuous, monotonic, and integer-valued only at integer arguments, then ⌊f(⌊x⌋)⌋ = ⌊f(x)⌋.

Analyze the prove: if f is continuous, monotonic, and integer-valued only at integer arguments, then ⌊f(⌊x⌋)⌋ = ⌊f(x)⌋..